Protein backbone dynamics from N-HN dipolar couplings in partially aligned systems: a comparison of motional models in the presence of structural noise

Residual dipolar couplings (RDCs) provide excellent probes for the exploration of dynamics in biomolecules on biologically relevant time-scales. Applying geometric motional models in combination with high-resolution structures to fit experimental RDCs allows the extraction of local dynamic amplitudes of peptide planes in proteins using only a limited number of data points. Here we compare the behaviour of three simple and intuitive dynamic modes: the Gaussian axial fluctuation model (1D-GAF), the two-site jump model, and a model supposing axially symmetric motion about a mean orientation. The requirement of a structural model makes this kind of methodology potentially very sensitive to structural imprecision. Numerical simulations of RDC dynamic averaging under different regimes show that the anisotropic motional models are more geometrically stringent than the axially symmetric model making it more difficult to alias structural noise as artificial dynamic amplitudes. Indeed, it appears that the model extracts accurate motional amplitudes even in the presence of significant structural error. We also show that a two-site jump model, also assuming the (alpha)C(i-1)-(alpha)C(i) as rotation axis, can only be distinguished from the previously developed GAF model beyond amplitude/jumps of around 40 degrees. The importance of appropriate estimation of the molecular alignment tensor for determination of local motional amplitudes is also illustrated here. We demonstrate a systematic scaling of extracted dynamic amplitudes if a static structure is assumed when determining the alignment tensor from dynamically averaged RDCs. As an example an artificial increase of 0.14 (0.85 compared to the expected 0.71) is observed in the extracted S2 if a pervasive 20 degrees GAF motion is present that is ignored in the tensor determination. Finally we apply a combined approach using the most appropriate motional model, to complete the analysis of dynamic motions from protein G.